Summary and Prospects

A summary of the present status of Brillouin–Wigner many-body methodology is given. Future prospects are assessed.

[1]  D. R. Bates,et al.  Spin-coupled theory of molecular wavefunctions: applications to the structure and properties of LiH(X1∑+), BH(X1∑+), Li2(X1∑g+) and HF(X1∑+) , 1977, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[2]  Ian M. Mills,et al.  Force Constants and Dipole-Moment Derivatives of Molecules from Perturbed Hartree-Fock Calculations. I , 1968 .

[3]  S. Chattopadhyay,et al.  Development of a linear response theory based on a state-specific multireference coupled cluster formalism , 2000 .

[4]  J. Pittner,et al.  Analytic gradient for the multireference Brillouin-Wigner coupled cluster method and for the state-universal multireference coupled cluster method. , 2007, The Journal of chemical physics.

[5]  J. Gerratt,et al.  Force Constants and Dipole‐Moment Derivatives of Molecules from Perturbed Hartree–Fock Calculations. II. Applications to Limited Basis‐Set SCF–MO Wavefunctions , 1968 .

[6]  Peter Pulay,et al.  Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules , 1969 .

[7]  Jürgen Gauss,et al.  Triple excitations in state-specific multireference coupled cluster theory: application of Mk-MRCCSDT and Mk-MRCCSDT-n methods to model systems. , 2008, The Journal of chemical physics.

[8]  S. Wilson,et al.  On the use of Brillouin-Wigner perturbation theory for many-body systems , 2000 .

[9]  S. Chattopadhyay,et al.  A state-specific approach to multireference coupled electron-pair approximation like methods: development and applications. , 2004, The Journal of chemical physics.

[10]  Kimihiko Hirao,et al.  Second-order quasi-degenerate perturbation theory with quasi-complete active space self-consistent field reference functions , 2001 .

[11]  J. Stephen Binkley,et al.  Theoretical models incorporating electron correlation , 2009 .

[12]  H. Schaefer,et al.  Brillouin-Wigner coupled cluster theory: Fock-space approach , 2002 .

[13]  Uttam Sinha Mahapatra,et al.  State-Specific Multi-Reference Coupled Cluster Formulations: Two Paradigms , 1998 .

[14]  Stephen Wilson,et al.  Theoretical chemistry and physics of heavy and superheavy elements , 2003 .

[15]  K. Hirao,et al.  A COMPLETE ACTIVE SPACE VALENCE BOND METHOD WITH NONORTHOGONAL ORBITALS , 1997 .

[16]  P. Mach,et al.  Many-body Brillouin–Wigner second-order perturbation theory: A robust and efficient approach to the multireference correlation problem† , 2007 .

[17]  Francesco A Evangelista,et al.  High-order excitations in state-universal and state-specific multireference coupled cluster theories: model systems. , 2006, The Journal of chemical physics.

[18]  Stephen Wilson,et al.  Electron Correlation in Molecules , 1984 .

[19]  J. Gerratt,et al.  General Theory of Spin-Coupled Wave Functions for Atoms and Molecules , 1971 .

[20]  Ivan Hubač,et al.  Size-extensivity correction for the state-specific multireference Brillouin–Wigner coupled-cluster theory , 2000 .

[21]  Francesco A Evangelista,et al.  Coupling term derivation and general implementation of state-specific multireference coupled cluster theories. , 2007, The Journal of chemical physics.

[22]  M. Plesset,et al.  Note on an Approximation Treatment for Many-Electron Systems , 1934 .

[23]  K. Hirao,et al.  Multireference perturbation theory with optimized partitioning. I. Theoretical and computational aspects , 2003 .

[24]  K. Hirao,et al.  On the performance of diagrammatic complete active space perturbation theory , 2000 .

[25]  Stephen Wilson,et al.  Algebraic approximation in many-body perturbation theory , 1976 .

[26]  P. Mach,et al.  Many-body Brillouin–Wigner second-order perturbation theory using a multireference formulation: an application to bond breaking in the diatomic hydrides BH and FH , 2006 .

[27]  Kimihiko Hirao,et al.  Recent Advances in Multireference Methods , 1999 .

[28]  S. Chattopadhyay,et al.  Applications of size-consistent state-specific multi-reference coupled cluster (SS-MRCC) theory to study the potential energy curves of some interesting molecular systems , 2004 .

[29]  J. Pittner,et al.  Multireference Brillouin-Wigner coupled cluster method with singles, doubles, and triples: efficient implementation and comparison with approximate approaches. , 2008, The Journal of chemical physics.

[30]  Uttam Sinha Mahapatra,et al.  A size-consistent state-specific multireference coupled cluster theory: Formal developments and molecular applications , 1999 .

[31]  R. Bartlett,et al.  Multireference many‐body perturbation theory , 1988 .

[32]  Wolfgang Wenzel,et al.  Excitation energies in Brillouin-Wigner-based multireference perturbation theory , 1998 .

[33]  H. Quiney,et al.  On the application of Brillouin-Wigner perturbation theory to a relativistic and non-relativistic hydrogenic model problem , 2001 .

[34]  Jiří Pittner,et al.  Continuous transition between Brillouin-Wigner and Rayleigh-Schrödinger perturbation theory, generalized Bloch equation, and Hilbert space multireference coupled cluster , 2003 .

[35]  Stephen Wilson,et al.  The group function model. A set of orthogonality conditions , 1976 .

[36]  K. Brueckner,et al.  Many-Body Problem for Strongly Interacting Particles. II. Linked Cluster Expansion , 1955 .

[37]  Michel Dupuis,et al.  A complete active space valence bond (CASVB) method , 1996 .